In this talk, we study the classical result ``The L^{2}-boundedness for the Cauchy integral operator on Lipschitz curves". The theorem was first proved by Calder?n (PNAS, 1977) when the Lipschitz curve has a small Lipschitz constant. The smallness assumption on the Lipschitz constant was later removed by Coifman-McIntosh-Meyer (Ann. Math., 1982). To give a motivation for this theorem, we study the Dirichlet problem for the Poisson equation in an arbitrary bounded Lipschitz domain. There are several proofs on the theorem of Coifman-McIntosh-Meyer. Here we follow a martingale proof given by Coifman-Jones-Semmes (JAMS, 1989). Necessary materials for this method will be given in this talk.